Question

P(x)=x^3+5x^2+2x-8 which three factors of the polynomail

Answer 1

(x - 1)(x + 2)(x + 4).

Explanation:

p(x)=x^3+5x^2+2x-8

p(1) = 1^3 + 5(1)^2 + 2(1) - 8

= 1 + 5 + 2 - 8 = 0, therefore (x - 1) is a factor (By the Factor Theorem).

Divide p(x) by x - 1:

x^2 + 6x + 8 <-------- is the quotient

x - 1 ) x^3 + 5x^2 + 2x - 8

x^3 - x^2

6x^2 + 2x

6x^2 - 6x

8x - 8

8x - 8

............

and x^2 + 6x + 8

= (x + 2)(x + 4).